{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Chebyshev polynomials"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as pt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part I: Plotting the Chebyshev polynomials"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = np.linspace(-1, 1, 100)\n",
        "\n",
        "pt.xlim([-1.2, 1.2])\n",
        "pt.ylim([-1.2, 1.2])\n",
        "\n",
        "for k in range(10): # crank up\n",
        "    pt.plot(x, np.cos(k*np.arccos(x)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part II: Understanding the Nodes\n",
        "\n",
        "What if we interpolate random data?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "n = 50 # crank up"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### \"Extremal\" Chebyshev Nodes (or: Chebyshev Nodes of the Second Kind)\n",
        "\n",
        "* Most often used for computation\n",
        "* Note: Generates $n+1$ nodes -> drop $k$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb75057fe80>]"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "k = n-1\n",
        "\n",
        "i = np.arange(0, k+1)\n",
        "x = np.linspace(-1, 1, 3000)\n",
        "\n",
        "def f(x):\n",
        "    return np.cos(k*np.arccos(x))\n",
        "\n",
        "nodes = np.cos(i/k*np.pi)\n",
        "\n",
        "pt.plot(x, f(x))\n",
        "pt.plot(nodes, f(nodes), \"o\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Chebyshev Nodes of the First Kind (Roots)\n",
        "\n",
        "* Generates $n$ nodes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb75061a668>]"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "i = np.arange(1, n+1)\n",
        "x = np.linspace(-1, 1, 3000)\n",
        "\n",
        "def f(x):\n",
        "    return np.cos(n*np.arccos(x))\n",
        "\n",
        "nodes = np.cos((2*i-1)/(2*n)*np.pi)\n",
        "\n",
        "pt.plot(x, f(x))\n",
        "pt.plot(nodes, f(nodes), \"o\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Observe Spacing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb750520470>]"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "pt.plot(nodes, 0*nodes, \"o\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part III: Chebyshev Interpolation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "V = np.cos(i*np.arccos(nodes.reshape(-1, 1)))\n",
        "data = np.random.randn(n)\n",
        "coeffs = la.solve(V, data)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb75066c1d0>]"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = np.linspace(-1, 1, 1000)\n",
        "Vfull = np.cos(i*np.arccos(x.reshape(-1, 1)))\n",
        "pt.plot(x, np.dot(Vfull, coeffs))\n",
        "pt.plot(nodes, data, \"o\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part IV: Conditioning"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1.4142135623730963"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "n = 10 # crank up\n",
        "\n",
        "i = np.arange(n, dtype=np.float64)\n",
        "nodes = np.cos((2*(i+1)-1)/(2*n)*np.pi)\n",
        "V = np.cos(i*np.arccos(nodes.reshape(-1, 1)))\n",
        "\n",
        "la.cond(V)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.3rc1"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}